Part 1: Motor-Loss Efficiencies
Maximum motor efficiency does not occur at either maximum torque or speed, nor does it occur at maximum mechanical power.
Motor Efficiency with Electrical Loss
Efficiency can be calculated based on electrical loss in the winding resistance. This efficiency for dc or PMS motors can be derived, beginning with the basic torque-speed equation for PMS and brush motors:
The "mechanically-referred flux linkage," L , is the basic quantity relating mechanical and electrical sides of the motor model, in much same way that turns ratio relates primary and secondary windings of transformers:
where w is the mechanical frequency, w me. R is winding resistance and vw is the winding induced (or "speed") voltage. (Winding current, i, must be measured in the same way that vw is, such that their product is power.)
Motor mechanical output power is
and electrical input power is
Then efficiency is the ratio of output to input power,
where w 0 is the no-load (maximum) motor speed at zero torque. For this idealized case, motor efficiency increases with speed and reaches 100 % at the no-load speed. The efficiency-speed curves are plotted below; the input and output powers are normalized by dividing them by their maximum values. Maximum output power occurs at w 0/2 and maximum input power at w = 0 (stall). At the two ends of the speed range, output power is zero, but at w 0, input power is also zero and h = 1. But h for zero input/output power is not very meaningful.
More realistically, electrical-loss efficiency is degraded further by two other kinds of losses: motor magnetic losses, and motor-drive loss.
Motor Efficiency with Magnetic Loss
Motor magnetic power loss consists of eddy-current and hysteresis losses. Eddy-current loss is minimized in a well-designed motor by the use of laminated armatures which minimize eddy currents induced in them. However, as speed increases, loss in the magnetic material (usually steel with 3 % silicon - "electrical steel") also increases by the square of the frequency. A resistance, Rm, shunting the induced voltage generator of the motor model dissipates vw 2/Rm, and the speed voltage, vw , is proportional to the motor speed.
Magnetic hysteresis loss is proportional to motor speed. The lost energy density is equal to the area of the magnetic B-H loop. Power loss varies with the loop traversal rate. Motors with more poles are cycled faster, with higher hysteresis loss. To model this loss, a current source shunting the induced voltage generator would sink power proportional to induced voltage and hence speed.
Our approximate magnetic-loss model will assume dominant eddy-current loss and use a shunt resistance, Rm, across the induced-voltage generator on the electrical side of the motor model, forming a resistive divider with R. Po is then modified to become
Then efficiency, including magnetic motor loss, becomes
and is plotted below, where h mx is h m for Rm = x× R.
As Rm increases relative to R, magnetic/electric loss decreases, efficiency increases and the peak approaches w 0.
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